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3 years ago

Find the area inside the semicircle and out side the triangle in terms of ń

Mathematics

1 answer:

Elan Coil [88]3 years ago

6 0

Answer:

π 169 / 2 - 120

Step-by-step explanation:

I'm assuming you are asking question about 24.

So first find radius of semicircle:

a^2+b^2=c^2

10^2+24^2=c^2

c=26

radius 26/2 = 13

Then let's calculate area of semicircle

area of circle = π*r^2

area of semicircle = π*r^2 / 2

area of given semi circle = π 169 / 2

Then let's calculate area of triangle

area of triangle = 10 * 24 / 2 = 120

Area of the shaded region = π 169 / 2 - 120

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Find x. (Finding an angle measure given extended triangles) Please help

Alja [10]

50+79=129
180-129=51
X=51

Explanations
Angles on a straight line add up to 180 degrees. So 180-101=79 degrees
50 degrees is an opposite angle so it moves into the internal angle.
Angles in a triangle add up to 180 so (180-50-79=51)
Ans is 51 I think

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Answer:

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Answer:

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Step-by-step explanation:

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3 years ago

1. What are the solutions (coordinate points) to the system of equations?

Leto [7]

Question 1

The given system of equations is:

$y = {x}^{2} + 5x + 6 \\ y = 3x + 6$

Equate the two equations:

${x}^{2} + 5x + 6 = 3x + 6$

Rewrite in standard form:

${x}^{2} + 5x - 3x + 6 - 6 = 0$

${x}^{2} + 2x = 0$

$x(x + 2) = 0$

$x = 0 \: or \: x = - 2$

When we put x=0, in y=3x +6, we get:

$y = 3(0) + 6 = 6$

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

$y = 3( - 2) + 6 = 0$

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

$f(x) = {x}^{6} - {x}^{4}$

Let us put x=-x,

$f( - x) = {( - x)}^{6} - {( - x)}^{4}$

This gives:

$f( - x) = {x}^{6} - {x}^{4}$

We can observe that:

$f(x) = f( - x)$

This is the property of an even function.

Question 3:

The given function is

$f(x) = {x}^{2} + 3x - 2$

The average rate of change of f(x) from x=a to x=b is given as:

$\frac{f(b) - f(a)}{b - a}$

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

$= \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11$